Binary Counter

So when I first started messing with electronics stuff I decided to try to understand things starting with the simplest components and working up from there.  I found a binary counter IC and wired together something to convert its binary counting to sequential counting by using transistors as digital logic gates.  I cheated a little bit and used some packaged IC NOR gates but still this is on a pretty fundamental level of digital logic.

DSC05143

The battery connected to the voltage regulator on the left goes to a 555 timer that is just pulsing a signal to the binary counter.  The battery also powers the red LEDs and if I remember correctly the other battery is to power the yellow LEDs because the voltage drop through the 555 and a red LED didn’t leave me with enough for another LED at the same time with the way it was wired. The outputs directly from the counter are displayed on the yellow LEDs and the same outputs pass through all the digital logic crap and light up the red LEDs sequentially.

Using these larger discrete components makes you realize how much goes into these small chips we have even for very simple functionality.  Just the 555 timer itself could be made with the same transistors and resistors I used for the logic parts here.  Take a look at this kit where you can do just that http://www.evilmadscientist.com/2013/555-kit/555 kit And here’s a video of the counter in action.  There’s an episode of Futurama playing in the background providing the somewhat epic commentary.

Testing CDF compatibility

The other day my friend noticed that for the first several pairs of consecutive integers, the difference of their cubes was prime.  I investigated the subject and am posting the Mathematica file to test CDF compatibility with the blog.

https://dl.dropboxusercontent.com/u/27794628/diffofcubes.html

Well wordpress.com is retarded and claims that embedding is not allowed “for security reasons”, so I guess I just have to link all my Mathematica work.

diffofcubes

What it came down to, in case anyone was wondering, is explained by the graph above.  The horizontal axis is in 100s of numbers, the vertical axis is the percentage of those numbers that are prime.  The red curve corresponds to the percentage of the odd integers which are prime (up to the first 1,000,000) and the blue curve is the percentage of the numbers generated by the difference of cubes of sequential integers which are prime (up to the first 1,000,000).  There doesn’t seem to be anything special about the difference of cubes of sequential integers with regards to primality.  Further explanation is in the link.